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; Appendix II. 861 * if E shew energy as delivered from a rifle bullet (W#2/2 g) while A, penetrating a target to depth 4 the pressure exerted at any point will be shewn by the/ ordinates. Therefore force is rate of energy change regarding distance. If, however, the curve/ be drawn to a time base as at D, summation will give momentum, or (W#/£•), for momentum = impulse or ft. Then, for a second definition, force is rate of change of momentum regarding time. These principles may be carried much further: thus, kinetic energy is the sum of \v regarding momentum and so on. Speaking next of curve averages, it will be easily seen that average velocity, for example, will depend on the base units, and that a time-base average can only equal a distance-base average in the case of uniform velocity, for then distances are proportional to times, and the curves are exactly alike (see E). Uniformly accelerated velocity is shewn at F for both time and distance bases, and the average v is evidently less in the former than the latter. In like manner there are time- and distance-base averages of force, as at D and c respectively, a steam-engine- indicator mean pressure being a distance average. {See p. 1099.) P. 478. Energy Curves. Example 63.—A steam piston of a horizontal engine is 30 ins. diameter, and the net propelling forces due to the steam in Ibs. per sq. in., at 6 in. intervals of stroke, are as follows : 100, 98, 97, 96, 95, 79, 67, 57, 49, 43, 3*, 34i, 3*, 28, 25, 23, 21, £c. The resistances of load and friction are 19 tons, assumed constant, and the weight of the moving parts is taken at 6 tons. Find the correct length of stroke and draw the velocity curve. (Hons. Applied Mechs. Exam., 1897, slightly altered.) Draw any horizontal base A B, Fig. 824, and set out the 6 in. spaces as shewn. Erect verticals, plot total net steam pressure in ton's =p (piston area--2240) = "315^, and draw hyperbolic curve C Q r>. As the piston advances from left to right, the area under this curve shews, total energy up to a given position. Summate then curve C Q D, and obtain curve A M F of total energy (see p. 860). The scale for B F is obtained from previous explanations. Draw G H so that AG = P the total load resistance, = 19 tons. Now, energy absorbed by load is P x D, where D is the stroke swept out up to any point, and the summation of G H, with same pole P, gives A L j, the curve of load energy measurable to same scale as B F. But generally—